WELLINGTON, New Zealand—The euro took an early morning tumble in Asia and traders are gearing up for more volatility after a first official projection of Greece's referendum outcome, based on early counting, indicated at least 61% of Greeks voted "no" to creditors' demands on Sunday.

The euro fell as low as $1.0979 against the greenback and is currently trading at $1.1015. The safe-haven Japanese yen benefited from the turmoil, with the euro falling to ¥ 133.76 and the U.S. dollar falling to ¥ 121.71.

Markets are skittish as the result "sharply raises the prospect of an eventual Greek exit from the eurozone," said BNZ FX Strategist Raiko Shareef. "Clearly, European leaders will not take this lightly."

He expects the euro to see more movement over the day but driven by information rather than improving liquidity. Investors will now be hunting for any clues on how European leaders respond, on the lookout for comments from high-ranking European officials and/or the European Central Bank, said Mr. Shareef. He said the pair has initial support at $1.0950.

"We will be in for a volatile day/week as the U.S. dollar and yen are being bought in safe haven trading," said Wellington-based OM Financial senior client adviser Stuart Ive. "We will remain focused on headlines and wary of Central Bank intervention."

Overall, the likely "no" outcome "leaves the market with more questions than answers," said ANZ Bank's Senior FX Strategist Sam Tuck.

While the projected outcome would strengthen the domestic standing of Greek Prime Minister Alexis Tsipras, who campaigned vehemently for Greeks to reject lenders' terms for further bailout funding, he may find it difficult to deliver on his promise to secure a more lenient bailout deal from Europe, where other governments, led by Germany, are in no mood to offer Greece more generous terms.

Mr. Tuck noted a number of European leaders were adamant that a "No" vote wouldn't strengthen Greece's position at the negotiating table, making future negotiations difficult and protracted. The European Central Bank may also find it difficult to extend—or even maintain—the ELA emergency funding if a deal between Greece and its creditors isn't close at hand, said Mr. Tuck.

"If the ECB does not extend additional ELA it is very difficult to see how the banks can open on Tuesday as planned and the economic crisis will intensify. Surely the probability of a Greek exit has now increased," he added.

Write to Rebecca Howard at rebecca.howard@wsj.com

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